A variant of Mathias forcing that preserves ACA0
François G. Dorais · 2012
We present and analyze Fσ-Mathias forcing, which is similar but tamer than Mathias forcing. In particular, we show that this forcing preserves certain weak subsystems of second-order arithmetic such as ACA0 and WKL0 + I� 0 2 , whereas Mathias forcing does not. We also show that the needed reals for Fσ-Mathias forcing (in the sense of Blass in Ann Pure Appl Logic 109(1-2):77-88, 2001) are just the computable reals, as opposed to the hyperarithmetic reals for Mathias forcing.